# Use a sign analysis to solve the following inequality 2x^3 < x^2+3x? .

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#### Explanation

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#### Explanation:

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1
Feb 9, 2018

]-oo, -3/2[uu]0,3[

#### Explanation:

$2 {x}^{3} < {x}^{2} + 3 x$

$2 {x}^{3} - {x}^{2} - 3 x < 0$

$x \left(2 {x}^{2} - x - 3\right) < 0$

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot 2 \cdot \left(- 3\right)}}{4}$

$x = \frac{- 1 \pm \sqrt{25}}{4}$

$x = \frac{- 1 \pm 5}{4}$

$x = - 1 \mathmr{and} x = - \frac{3}{2}$

The second-degree polynomial will be negative in ]-3/2,-1[

$\textcolor{w h i t e}{\ldots \ldots \ldots . .} - \infty \ldots . . - \frac{3}{2.} \ldots . . - 1. \ldots \ldots .0 \ldots \ldots \ldots \ldots$
$x \textcolor{w h i t e}{\ldots - -} - - - - - - - - - 0 + + + + + + + +$
$p o l y n o m i a l \textcolor{w h i t e}{.} + + + 0 \textcolor{w h i t e}{.} - - 0 + + + + +$
$g i v e s \textcolor{w h i t e}{.} - - - - - 0 \textcolor{w h i t e}{.} + + 0 - - 0 + + + + +$

]-oo, -3/2[uu]0, +oo[

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